Although, as said before, it might be a bit chilly, but I think around November is the best time to travel. Less tourists, no sweaty people and stinky people around you I had many friends travel by train in China (incl solo female travelers), but I would prefer flying. More options in departure times, although it might cost more and need to travel to airport - downtown.

Don't worry ...relax...China changed a lot and is really safe, but ofcourse don't leave your brain behind as nickyboy said